Final answer:
Yes, other composers were alive when Beethoven was alive. Both his predecessors, like Haydn and Mozart, and successors of the Romantic era such as Wagner and Brahms were contemporaries at different points in his life.
Step-by-step explanation:
Beethoven's time as a composer bridged the gap between the Classical and Romantic periods in music history. He influenced many future composers, and others were contemporaries to him. During Beethoven's lifetime, composers such as Haydn and Mozart were first famous, with Haydn being a major influence and eventually also his teacher.
However, there were also many significant composers born during or shortly after Beethoven's time who were part of the Romantic era. This era was characterized by composers like Brahms, Tchaikovsky, Schumann, Schubert, Chopin, and Wagner, who indeed were alive during Beethoven's later years or were born in that period and took inspiration from Beethoven's later, more Romantic-style compositions.
On the one hand, you have composers like Haydn and Mozart, who were of the older generation but whose lives overlapped with Beethoven's. On the other hand, you have composers of the Romantic era like Strauss and Wagner, who were born later but still during Beethoven's lifetime and were influenced by his innovative transition to Romanticism. Therefore, the answer to the question is 'a) Yes,' as other famous composers were indeed alive during Beethoven's lifetime, either as his seniors or juniors in the timeline.